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Weir was reserve Fly-Half for Scotland's 2013 Six Nations campaign but with Scotland failing to score tries, Weir's Glasgow teammate Ruaridh Jackson was dropped and Weir stepped in. He started Scotland's final two games in the Championship which Scotland finished in third place.

Aged 22 and having recovered from a broken leg, Weir was starting Fly-half for Scotland's 2014 Six Nations having impressed in Glasgow's successful season. He scored a last minute Drop-goal to beat Italy in Rome for the first time since 2006.
In March 2014, Weir signed a new two-year contract with Glasgow. Glasgow coach and former Scotland Fly-half Gregor Townsend said

"We are delighted that Duncan has committed to the club for the next two seasons and this is really good news for us and for Scottish rugby. He has made a great return from injury this season and has been a consistent performer for the club and for Scotland during this year’s RBS 6 Nations. His drop-goal to win the Italy game was top drawer and he has shown that he can operate at the highest level of the game. Duncan works hard at getting better every day at training and he’s made great strides in both the technical and tactical side of playing at stand-off. His ability to lead the attack is beginning to become a real strength of his game. He has a big role to play at the club over the next couple of years."[4]